Okay, we are tasked with adding 9534 and 982. Let's begin!

Step 1: We'll start by adding the digits 4 & 2 in column 1 and get 6.

Step 2: We'll start by adding the digits 3 & 8 in column 2 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 5 & 9 in column 3 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 9 & 0 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 9534 + 982 = 10516.

